\newproblem{lay:4_6_15}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.6.15}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	If $A$ is a $3\times 7$ matrix, what is the smallest possible dimension of $\mathrm{Nul}\{A\}$?
}{
  % Solution
	By the Rank Theorem we know that for a $m\times n$ matrix
	\begin{center}
		$\dim\{\mathrm{Nul}\{A\}\}+\mathrm{Rank}\{A\}=n$
	\end{center}
	The rank cannot be larger than 3, so the dimension of $\mathrm{Nul}\{A\}$ cannot be smaller than 4, i.e., $\dim\{\mathrm{Nul}\{A\}\}\geq 4$.
}
\useproblem{lay:4_6_15}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
